The invention generally relates to an arrangement and a method for identifying the parameters of a nonlinear model of an electro-magnetic transducer and for using this information to correct the transfer characteristics of this transducer between input signal v and output signal p by changing the properties of the electro-magnetic transducer in design, manufacturing and by compensating actively undesired properties of said transducer by electric control. The electro-magnetic transducer may be used as an actuator (e.g. loudspeaker) or as a sensor (e.g. microphone) having an electrical input or output, respectively.
Most loudspeakers, headphones and other electro-acoustical devices use an electro-dynamical transducer with a moving voice coil in a static magnetic field. Models have been developed for this kind of transducer which provide sufficient accuracy for measurement and control application, such as disclosed in U.S. Pat. Nos. 4,709,391, 5,438,625, 6,269,318, 5,523,715, DE 4336608, U.S. Pat. Nos. 5,528,695, 6,931,135, 7,372,966, 8,019,088, WO2011/076288A1, EP 1743504, EP 2453670, EP 2398253 and DE 10 2012 020 271.
Electro-magnetic transducers converting an electric signal into a mechanic signal and vice versa use a coil at a fixed position and a moving armature connected via a driving pin with a diaphragm. This kind of transducer has some desired properties (e.g. high efficiency) which are not found in electro-dynamical transducers. The nonlinearities inherent in the electro-magnetic principle are a source of signal distortion. This disadvantage can be partly reduced by using a “balanced” armature using additional magnets.
Straightforward distortion measurement techniques reveal harmonic distortion and other symptoms of nonlinearities inherent in this transducer. However, the results of these measurements do not give a complete description of the nonlinear transfer behavior but depend on the particular properties of the excitation stimulus. An accurate model of the electro-magnetic transducer is required to get a deeper insight in the physical causes and to predict the large signal performance for any input signal. The theory developed for electro-dynamical transducers is not applicable for electro-magnetic transducers. F. V. Hunt developed a first nonlinear model in “Electroacoustics—The Analysis of Transduction and Its Historical Background” (Acoustical Society of America, New York, 1954, 1982), which describes the electro-magnetic transducer by an electrical equivalent circuit comprising lumped elements. The inductance L(x), transduction factor T(x) and magnetic stiffness Kmag(x) depend on the position x of the armature. This model was used by J. Jensen, et. al. in the paper “Nonlinear Time-Domain Modeling of Balanced-Armature Receivers,” published in the J. Audio Eng. Soc. Vol. 59, No. 3, 2011 March to predict the generation of odd-order harmonic distortion by assuming a symmetrical rest position of the armature in the magnetic field. All parameters are derived from the geometry of an ideal transducer having a magnetic material without saturation and hysteresis. The prior art has not disclosed a measurement technique for identifying the free parameters of this model applicable to real transducers.